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# Sample Size Determination

### Determine the smallest sample size required to estimate the population mean

Determine the smallest sample size required to estimate the population mean under the following specifications: a. e = 2.4 confidence level = 80% data between 50 and 150 d. e = 1.2 confidence level = 90%, data between 25 and 175 How do I find the third piece of information to use e= "Ï?" /(â??ð'?)? How do I es

### Use of Confidence Intervals and Sample Size Determination

The Modulus of rupture (MOR) for a particular grade of pencil lead is known to have a standard deviation of 250 psi. a. A random sample of 16 pencil leads yielded a sample mean of 6490. Construct a 90% confidence interval for the true mean MOR. b. Find the sample size required to estimate the true mean MOR to within ± 100 u

### Inspection of soft drinks

If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liter bottles to within + or - 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?

### Sample Size Calculation: Election Examples

A researcher wishes to estimate the proportion of eligible voters who will vote for a particular candidate in the upcoming election: a) How large should the sample size be so that a 85% confidence interval for the population proportion has a margin of error of 0.05. Assume that a preliminary sample suggests the proportion is

### Sample size of mean time for seniors who watch television

A survey is being planned to estimate, with a 98% confidence interval, the mean amount of time per week that seniors spend watching television. The population standard deviation is known to be 5.2 hours. What sample size will be required to obtain estimate that is within 0.5 hours of the population mean? Please see the attached

### Environmental Protection Agency (EPA) study for levels of carbon monoxide

6. Read the following statement and answer the questions that follow. 'The Environmental Protection Agency (EPA) is interested in determining the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. The EPA took a random sample of 1201 Americans and discovered that 1139 of them lived in

### Statistics

A researcher is interested in estimating the noise levels in decibels at area urban hospitals. She wants to be 90% confident that her estimate is correct. If the standard deviation is 4.13, how large a sample is needed to get the desired information to be accurate within 0.68 decibels?

### Confidence Level and Sample Size

A film alliance used a random sample of 50 U.S. citizens to estimate that the typical American spent 78 hours watching videos and DVDs last year. The standard deviation of this sample was 9 hours. How large a sample should be used to be 90 percent confident the sample mean is within 1.0 hour of the population mean? (Round yo

### Sample Size for Population Proportion..

You are asked by the owner of the Starshine Motel to develop a customer satisfaction survey to determine the percentage of customers who are dissatisfied with service. In the past year, 20,000 customers were serviced. She desires a 95% level of confidence with an allowable statistical error of +/- 0.02. From past estimates, th

### Survey sample size

7-6. Before spending huge sums to advertise to car owners that they should fill their tires with nitrogen, it would be wise to conduct a survey to determine the percentage of car owners who would pay for the nitrogen. How many randomly selected car owners should be surveyed? Assume that we want to be 90% confident that the sam

### Determining Sample Size: 95 Percent Confidence

A consumer group wants to estimate the mean electric bill for the month of July for single family-homes in a large city. Based on studies conducted in other cities, the standard deviation is assumed to be \$25. The group wants to estimate the mean bill for July to within + or - \$5 with 99% confidence. a. What sample size is ne

### Sample size from a survey of food costs per year

You are trying to estimate the average amount a family spends on food during a year. In the past, the standard deviation of the amount a family spends on food during the year has been approximately \$1,500. a. If you want to be 95% sure that you have estimated average family food expenditures within \$100, how many families do

### Statistics 1: 10 problems of confidence intervals, sample sizes, distribution

You work for a consumer advocate agency and want to find the mean repair cost of a washing machine. As part of your study, you randomly select 45 repair costs and find the mean to be \$117.00. The standard deviation is \$18.90. Complete parts (a) and (b). a. Construct a 90% confidence interval for the population mean repair cost

### Margin of Error and Sample size..

8. Suppose that it is a presidential election year and Ohio is one of the 'swing' states. Your polling company wants to conduct a presidential preference poll of the citizens of Ohio to predict which candidate will win the election. a. How many voters must be polled to be 95% confident of your results within +/- 3%? b. Ho

### How many subjects need to be enrolled in each group of a randomized clinical trial?

The Physician's Health Study was a randomized clinical trial, one of whose goals was to effect of cigarette smoking on the development of myocardial infarction preventing myocardial infarction (MI). Suppose that the incidence of MI is 0.005 per year among subjects who are actually take placebo and that aspirin prevents 20% o

### Sample size for a 99% confidence interval: collect sales tax on internet commerce

Many states are carefully considering steps that would help them collect sales taxes on items purchased through the Internet. How many randomly selected sales transactions must be surveyed to determine the percentage that transpired over the Internet? Assume that we want to be 99% confident that the sample percentage is within t

### Sample Size: U.S. Rental Car Mileages

Choosing an appropriate sample size: A consumer advocacy group is doing a large study on car rental practices. Among other things, the consumer group would like to estimate the mean monthly mileage, mu, of cars rented in the U.S. over the past year. The consumer group plans to choose a random sample of monthly U.S. rental ca

### Sample Size of Study Incomes in a Region

(TCO 1) An economist is interested in studying the incomes of consumers in a particular region. The economist needs to know how large a sample should be taken so that a 95% confidence interval for their mean income with an error of \$100 can be constructed. If the population standard deviation is known to be \$5,000 what sample

### Find sample size

A private medical clinic wants to estimate the true mean annual income of its patients. The clinic estimates that the true population standard deviation is around \$2300. If the confidence level is 95%, find the required sample size to meet the desired accuracy.

### Determining Necessary Sample Size

An automobile dealership plans to conduct a survey to determine what proportion of new-car buyers continue to have their cars serviced at the dealership after the warranty period ends. It estimates that 30 percent of customers do so. It wants the results of its survey to be accurate within 5 percent, and it wants to be 95 percen

### Determining Sample Size: Income Example

An economist is interested in studying the incomes of consumers in a particular region. The economist needs to know how large a sample should be taken so that a 90% confidence interval for their mean income with an error of \$500 can be constructed. If the population standard deviation is known to be \$8,000 what sample size wou

### Simulate the average hourly number of sales at the Kard Shop (Monte Carlo)

Kard Shop Hour No. Sales 9 60 10 70 11 47 Noon 53 1 80 2 70 3 50 4 60 Simulate the average hourly number of sales at the Kard Shop (Monte Carlo) for 50 hours. How does this number compare to the e

### Calculate SST for 4 observed values of a dependent variable

You have 4 observed values of the dependent variable in your sample. The values are 1, 2, 4, and 5. Calculate the SST. a) The SST is between 1 and 50 b) The SST is between 51 and 100 c) The SST is between 101 and 200 d) The SST is above 200 e) Not enough information provided Please explain!

### Bride's magazine: Sample Size for wedding cost if desired margin

Bride's magazine reported that the mean cost of a wedding is \$25,000. Assume that the population standard deviation is \$8400. Bride's plans to use an annual survey to monitor the cost of a wedding. Use 99% confidence. What is the recommended sample size if the desired margin of error is \$651.

### Sample size for estimation of population proportion

I am about to ask MTV viewers the following question: "Do you regularly watch MTV's Beavis and Butthead?" Last week I asked 100 of my friends the same question and 35 of them said yes. How many actual viewers must be surveyed to be 95% confident that the estimate of the viewership is in error by at most 3%? (Assume 100% res

### Job Satisfaction Survey - Determination of Sample Size

1. Need to provide an overview of the contents of the Research Paper and apply the concepts to the Job Satisfaction Survey attached. 2. Cover the concept of the techniques used to estimate sample size. 3. Determine the required sample size for estimating a single population mean. 4. Conclusion [Please refer to the

### Sample Size for Average ATM Cash Withdrawal Study

Last year a study showed that the average ATM cash withdrawal took 65 seconds with a standard deviation of 10 seconds. The study is to be repeated this year. How large a sample would be needed to estimate this year's mean with 95 percent confidence and an error of +-4 seconds?

### Comparing percentages with different sample sizes

25 groups with 7 people in each group, join "The Greatest Loser" competition. Based on the greatest percent of weight loss, the greatest loser wins. Calculations regarding percentages are made by taking the total weight of the group and dividing by 7. Weignts are measured initially and after 9 weeks. A new group comes alon

### Sample size and estimates

Find the minimum sample size n needed to estimate &#956; for the given values of c,s and E. C= 0.90, s,=8.7, and E=2 Assume that the preliminary sample has at least 30 members. n=___ (round to the nearest whole number)

### Sample Size: Birth Weight of Infants

A health care professional wishes to estimate the birth weight of infants. How large a sample must she select if she desires to be 90% confident that the true mean is within 6 ounces of the sample mean? The standard deviation of the birth weights is known to be 8 ounces.